Robust Watermarking Using Hybrid Transform of DCT, Haar and Walsh and SVD

International Journal of Engineering Research and Development

e-ISSN: 2278-067X, p-ISSN: 2278-800X, www.ijerd.com

Volume 10, Issue 12 (December 2014), PP.75-92

75

Robust Watermarking Using Hybrid Transform of DCT, Haar

and Walsh and SVD

Dr. H. B. Kekre1, Dr. Tanuja Sarode

2, Shachi Natu

3

1Senior Professor, Computer Engg. Dept., MPSTME, Vileparle, Mumbai, India.

2Associate Professor, Computer Dept. TSEC, Bandra, Mumbai, India.

3Ph. D. Research Scholar, MPSTME, Vileparle, Mumbai, India.

Abstract:- In this paper a novel approach of watermarking using hybrid transform and SVD is proposed.

Hybrid transform is generated from existing orthogonal transforms of different sizes by taking their kronecker

product. DCT, Walsh, and Haar transforms are used to generate the hybrid transforms DCT-Walsh, Walsh-

DCT, DCT-Haar, Haar-DCT, Walsh-Haar andHaar-Walsh. Each hybrid transform is applied column wise/row

wise on host. Singular Value Decomposition of watermark is obtained and first few singular values of

watermark are embedded in middle frequency band of hybrid column/row transformed host. Robustness of

proposed approach is evaluated against image compression, cropping, noise addition, image resizing and

histogram equalization attack. Performance of hybrid transform shows improvement against compression attack

by 59%, against noise addition by 70% and against resizing by 32-56% when compared to hybrid wavelet

transforms.

Keywords:- Watermarking, Singular Value Decomposition, Hybrid transform, Kronecker product, Hybrid

wavelet transform

I. INTRODUCTION Due to use of internet technology, vast amount of information is generated with a single click. Security

of this information is equally important. Usually availability of various tools makes distribution and

manipulation of digital information very easy. This may lead to claiming the digital information by someone

else other than owner. To avoid this, some technique is required wherein the information of owner can be

embedded in the digital information to be transmitted thus preventing illegal claim of ownership or can detect

any alterations done in the digital information. Watermarking fulfils this need. Different types of information

like identity of owner, logo of company etc. can be embedded in the information to be protected. The

information to be protected is called host or cover and the secret information embedded in it is called as

watermark. Depending on type of cover, watermarking can be classified as digital image watermarking, audio

and video watermarking. In the proposed work focus is on watermarking of digital images. Depending on how

the watermark is embedded in image, it is classified as spatial domain and frequency domain watermarking.

Spatial domain watermarking directly deals with pixel intensities of image. Frequency domain watermarking

first converts image into another form i.e. its frequency representation using transformation techniques and then

changes those frequency coefficients in such a way that hidden watermark goes unnoticeable with host. Some

more classifications of watermarking include visible and invisible watermarking. As the name suggests it either

reveals or hides the existence of watermark in host image depending on the purpose for which it is used. Robust

and fragile watermarking is yet another category of image watermarking. In robust watermarking, any change in

the host will try to prevent destruction of hidden watermark. Thus attacker cannot easily change or remove

hidden watermark to change the ownership information. In fragile watermarking, small change to image

information will easily damage the hidden watermark thereby detecting the unauthorised changes in contents of

host. Varieties of watermarking techniques available in literature are overviewed in the next section.

II. REVIEW OF LITERATURE In literature many spatial domain techniques were initially introduced to hide the watermark. Though

spatial domain techniques are not as robust as frequency domain techniques, due to their simplicity they are still

attracting the researchers. Some such spatial domain techniques have been presented in [1], [2], [3] and [4]

where LSB of host is used to hide MSB of watermark. To improve the robustness, instead of using LSB, 3rd or

4th LSB are preferred to hide the watermark. Also operations like shifting the watermark bits or embedding

watermark bits multiple times at different positions in host are proposed.

To have robust watermarking where watermarks can survive the attacks on digital contents, we need to

move to frequency domain watermarking. Transforms like DCT [5], [6], [7], Discrete wavelet transforms (DWT)

[8], [9], [10], Singular Value Decomposition [11], [12] are some of the popularly used transformation

Robust Watermarking Using Hybrid Transform of DCT, Haar and Walsh and SVD

76

techniques. Wavelet packet transform is also efficiently used for watermarking by Bhatnagar et al. in [13].

Using more than one transform has also shown a positive effect on robustness. Some popular pairs of such

multiple transforms are DWT-DCT [14], DWT-SVD [15], DCT-SVD [16], DWT-DCT-SVD [17] etc.

Cox [18] first introduced a watermarking using DCT. Piva et al. proposed watermarking using DCT in

[19] in which, a DCT domain watermarking of colour images is presented, which exploits the characteristics of

the human visual system and the correlation between the RGB image channels.Bedi et al. proposed a SVD and

DCT_DWT watermarking technique in [20]. The middle band DCT coefficients are chosen to achieve high

robustness against JPEG compression. Robustness against other attacks is achieved by taking DWT of the DCT

coefficients and the lowest frequency LL band of DWT is chosen for insertion. Chandra Mohan and Srinivas

Kumar presented a SVD based watermarking method in which watermark embedding is carried out in left

singular matrix U and diagonal matrix D [21]. Watermark image is embedded in the D component using Dither

quantization. A copy of the watermark is embedded in the columns of U matrix using comparison of the

coefficients of U matrix with respect to the watermark image. If extraction of watermark from D matrix is not

complete, there is a fair amount of probability that it can be extracted from U matrix.

Rahman proposed a DWT-DCT-SVD based watermarking method in [22]. In their watermarking

method, theoriginal image is rearranged using zigzag sequence and DWT is applied on rearranged image. Then

DCT andSVD are applied on all high bands LH, HL and HH. Watermark is embedded by modifying the

singularvalues of these bands. One more DWT-SVD based watermarking algorithm is proposed by Erkan Yavuz

and Ziya Telatar. In their method [23], third level decomposition of host image is obtained. LL and HL sub

bands obtained through this decomposition are used to embed singular values of watermark. In addition,

components of U matrix of watermark are embedded into LH and HH sub band. While extracting, first the

similarity of extracted U components are checked with the original one. If they are found similar, watermark is

constructed by using extracted singular values and original U and V matrices of the watermark.

Kekre, Tanuja and Shachi presented a DWT-DCT-SVD based hybrid watermarking method for colour

images in [24]. In their method, robustness is achieved by applying DCT to specific wavelet sub-bands and then

factorizing each quadrant of frequency sub-band using singular value decomposition. Watermark is embedded

in host image by modifying singular values of host image. Performance of this technique is then compared by

replacing DCT by Walsh in above combination. In [25], DCT wavelet transform of size 256*256 is generated

using existing well known orthogonal transform DCT of dimension 128*128 and 2*2. This DCT Wavelet

transform is used in combination with the orthogonal transform DCT and SVD to increase the robustness of

watermarking. HL2 sub-band is selected for watermark embedding. Performance of this proposed watermarking

scheme is evaluated against various image processing attacks. In [26] Walsh wavelet transform is used that is

derived from orthogonal Walsh transform matrices of different sizes. 256*256 Walsh wavelet is generated using

128*128 and 2*2 Walsh transform matrix and then using 64*64 and 4*4Walsh matrix which depicts the

resolution of host image taken into consideration. It is supported by DCT and SVD to increase the robustness.

Walsh wavelet based technique is then compared with DCT wavelet based method given in [25]. In [27], other

wavelet transforms like Hartley wavelet, Slant wavelet, Real Fourier wavelet and Kekre wavelet were explored

by Kekre, Tanuja and Shachi. Performance of Slant wavelet and Real Fourier wavelet were proved better for

histogram Equalization and Resizing attack than DCT wavelet based watermarking in [25] and Walsh wavelet

based watermarking presented in [26].

III. HYBRID TRANSFORM AND SVD Hybrid transform is generated by taking kronecker product of two different orthogonal transforms of

different sizes. For example, DCT-Walsh hybrid transform is generated using DCT and Walsh transform matrix.

DCT-Walsh hybrid transform matrix of size say 256x256 can be generated using DCT matrix of size 128x128

and Walsh matrix of size 2x2. Thus (128, 2) is one possible pair of component matrix size. Similarly other

possible pairs are (64, 4), (32, 8), (16, 16), (8, 32) (4, 64) and (2,128). It comprises of the good characteristics of

both the component transforms and hence is expected to shoe better performance than individual component

transform. In the proposed approach component transforms of size 16x16 each is used to generate 256x256

hybrid transform matrix.

Using singular value decomposition, any real matrix A can be decomposed into a product of three

matrices U, S and V as A=USVT, where U and V are orthogonal matrices and S is diagonal matrix. If A is mxn

matrix, U is mxm orthonormal matrix whose columns are called as left singular vectors of A and V is nxn

orthonormal matrix whose columns are called right singular vectors of A. Some properties of SVD which make

it useful in image processing are:

The singular values are unique for a given matrix.

The rank of matrix A is equal to its nonzero singular values. In many applications, the singular values of

a matrix decrease quickly with increasing rank. This property allows us to reduce the noise or compress the

matrix data by eliminating the small singular values or the higher ranks [28].


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The singular values of an image have very good stability i.e. when a small perturbation is added to an

image; its singular values don’t change significantly [29].

IV. PROPOSED METHOD In the proposed method, a hybrid watermarking approach using SVD and hybrid transform is proposed.

Use of orthogonal transforms like DCT, DFT, and Haar with SVD is very popular. In this paper a concept of

hybrid transforms generated from orthogonal transforms is used to perform watermarking. Strength of hybrid

transform is increased by using SVD with it. Hybrid transform is applied to host image either column wise or

row wise. Middle frequency band of transformed host is selected to embed the watermark. Watermark to be

embedded in host is subjected to SVD. Since maximum of image energy is accumulated in only first few

singular values, these values are sufficient to embed the watermark in host. In propose approach we find that for

128x128 size watermark image, first 30 singular values contain almost 99.99% of image energy and hence

sufficient for embedding. Before embedding, singular values are adaptively scaled to match their energy with

the energy of middle frequency region in which they are embedded. Inverse transform of host after embedding

singular values in it gives watermarked image.

Extraction of watermark is followed exactly in reverse manner. Thus watermarked image is first

column/row transformed using hybrid transform. From its middle frequency region, singular values of

watermark are obtained. These singular values are scaled up to bring them back to their original strength.

Inverse SVD of these scaled singular values gives us recovered watermark. Robustness of proposed approach is

tested by comparing recovered watermark with embedded one. Comparison is done on the basis of average of

absolute difference between pixels of two images known as Mean Absolute Error (MAE).

Proposed approach of watermarking is tested for its robustness against the attacks like image compression,

image cropping, adding noise to watermarked images, resizing watermarked images and equalizing histogram of

watermarked images. Fig. 1 shows five different host images and a watermark used to embed in host images.

(a) Lena (b) Mandrill (c) Peppers (d) Face (e) Puppy (f) NMIMS

Fig. 1: (a)-(e) host images (f) watermark image used for experimental work

Fig. 2 shows the watermarked image Mandrill using each of the column hybrid transforms mentioned and

extracted watermark NMIMS from it without performing any attack. Below each watermarked image, MAE

between host and watermarked image is displayed and below each extracted watermark, MAE between

embedded and extracted watermark is shown.

Watermarked

image

Extracted

watermark

Watermarked

image

Extracted

watermark

MAE=0.337 MAE=0 MAE=0.265 MAE=0

DCT-Walsh hybrid column transform Walsh-DCT hybrid column transform

MAE=0.304 MAE=0 MAE=0.131 MAE=0

DCT-Haar hybrid column transform Haar-DCT hybrid column transform


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MAE=0.223 MAE=0 MAE=0.136 MAE=0

Walsh-Haar hybrid column transform Haar-Walsh hybrid column transform

Fig. 2: watermarked image Mandrill and extracted watermark

V. RESULT ANALYSIS AGAINST ATTACKS A. Compression attack

Compression of watermarked images is very obvious as its main aim is to save bandwidth. In proposed

approach three types of compressions are performed. Compression using transforms like DCT, DST, Walsh,

Haar and DCT wavelet, Compression using Vector quantization and JPEG compression. In compression using

VQ, Kekre’s Fast Codebook Generation (KFCG) algorithm [30] is used to generate codebook of size 256. JPEG

compression includes compression using quality factor 100. One such compression results are shown here in Fig.

3. For each of the column hybrid transform mentioned, results of DCT compression are presented.

Watermarked

image after

compression

Extracted

watermark

Watermarked

image after

compression

Extracted

watermark

MAE=2.895 MAE=3.259 MAE=2.895 MAE=3.589

DCT-Walsh Walsh-DCT

MAE=2.895 MAE=3.768 MAE=2.895 MAE=2.505

DCT-Haar Haar-DCT

MAE=2.895 MAE=9.789 MAE=2.894 MAE=4.811

Walsh-Haar Haar-Walsh

Fig. 3: Results of various hybrids transforms against compression using DCT

From Fig. 3 it can be seen that different hybrid transforms give different MAE values between

embedded and extracted watermark and each of them is showing quite acceptable quality of extracted

watermark. Table 1 shows average MAE between embedded and extracted watermark extracted from five

different host images against compression attack when column and row version of hybrid transforms are used to

embed the watermark.


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Table I: Average MAE between embedded and extracted watermark against compression attack

using various hybrid transforms

Compression using

Column DCT-Walsh

Column Walsh-DCT

Column DCT-Haar

Column Haar-DCT

Column Walsh-

Haar

Column Haar-Walsh

DCT 1.657 1.527 1.817 1.234 2.931 1.905

DST 1.677 1.537 1.840 1.265 2.980 1.980

Walsh 0 1.752 0.449 1.832 1.442 0.170

Haar 0.828 2.969 0.9 2.832 2.886 1.181

DCT Wavelet 7.182 2.015 7.716 1.407 8.569 8.082

JPEG 46.061 43.189 45.190 43.144 44.883 41.886

VQ 41.250 40.758 40.619 33.096 40.764 27.405

Compression using

Row DCT-

Walsh

Row Walsh-

DCT

Row DCT-

Haar

Row Haar-

DCT

Row Walsh-

Haar

Row Haar-

Walsh

DCT 2.197 1.482 3.312 2.230 1.981 3.449

DST 2.135 1.502 3.339 2.258 2.054 3.532

Walsh 0.327 2.010 2.062 2.253 1.136 1.660

Haar 3.131 2.756 4.057 3.491 1.110 2.690

DCT Wavelet 11.640 2.145 11.423 2.115 9.925 12.077

JPEG 47.069 44.216 45.964 39.436 45.100 40.968

VQ 39.648 40.637 39.832 30.429 40.897 34.998

From Table I it can be seen that except JPEG compression and VQ based compression, against all other

types of compression attacks, all explored hybrid transforms show strong robustness.

B. Cropping Attack

Watermarked images are cropped at different regions: at corners and at centre. 16x16 size squares and

32x32 size squares are cropped at the corners of watermarked image to observe the effect of cropping more

information. 32x32 size square is cropped at the centre where number of pixels cropped is same as in case of

cropping 16x16 pixels at four corners. Fig. 4 shows the result images for cropping 32x32 at centre attack using

column hybrid transforms.

Watermarked

image after

cropping

Extracted

watermark

Watermarked

image after

cropping

Extracted

watermark

MAE=1.856 MAE=61.781 MAE=1.856 MAE=165.969

DCT-Walsh Walsh-DCT

MAE=1.856 MAE=25.533 MAE=1.856 MAE=0

DCT-Haar Haar-DCT


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MAE=1.856 MAE=144.594 MAE=1.855 MAE=0


Fig. 4: Results of various hybrid transforms against cropping 32x32 portion at centre.

From Fig. 4 it is observed that when Haar is used as base transform (first component) during generation

of hybrid transform, highest robustness against cropping attack is obtained. Thus Haar-DCT and Haar-Walsh

column hybrid transform show excellent robustness against cropping. On the other hand Walsh when used as

base transform in the generation of hybrid transform cannot withstand the cropping attack. In case of row

versions of hybrid transforms also transforms having Haar as base transform perform very well against cropping

attack.

Table II shows Average MAE between embedded and extracted watermark against cropping attack for

column and row versions of hybrid transforms.

Table II: Average MAE between embedded and extracted watermark against cropping attack using

various hybrid transforms

Cropping type

Column DCT-Walsh

Column Walsh-DCT

Column DCT-Haar

Column Haar-DCT

Column Walsh-Haar

Column Haar-Walsh

16x16 at corners

58.328 55.231 51.901 115.660 55.613 123.134

32x32 at corners

35.162 27.042 33.539 242.896 26.898 260.219

32x32 at centre

71.125 95.420 61.814 0.749 90.048 0

Cropping type

Row DCT-

Walsh

Row Walsh-

DCT

Row DCT-

Haar

Row Haar-

DCT

Row Walsh-

Haar

Row Haar-

Walsh

16x16 at corners

56.626 36.456 49.493 73.904 29.773 83.985

32x32 at corners

34.500 45.407 35.560 254.603 46.026 281.515

32x32 at centre

48.616 51.125 45.665 1.885 41.382 3.048

From Table 2 it can be concluded that for cropping at centre, hybrid transform column as well as row

with Haar as the base transform shows strong robustness.

C. Noise addition attack

Two types of noises binary distributed run length noise and Gaussian distributed run length noise are

added to watermarked images. Binary distributed noise is added with different run length like 1 to10, 5 to 50

and 10 to 100. Fig. 5 shows the watermarked images with Gaussian distributed noise added to them and

watermark extracted from them when different hybrid transforms are used to embed the watermark.

Watermarked

image after

compression

Extracted watermark

Watermarked

image after

compression

Extracted

watermark

MAE=0.746 MAE=1.968 MAE=0.746 MAE=2.213


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Fig. 5: Results of various hybrid transforms against Gaussian distributed run length noise.

From Fig. 5 it is observed that column hybrid transforms show excellent robustness against Gaussian

distributed run length noise added to watermarked images. For binary distributed run length noise also, hybrid

transforms shoe very well sustenance. Table 3 shows average MAE between embedded and extracted watermark

from five different host images using column and row version of hybrid transforms.

Table III Average MAE between embedded and extracted watermark against noise addition attack using

various hybrid transforms

Noise type Column DCT-

Walsh

Column Walsh-DCT

Column DCT-Haar

Column Haar-DCT

Column Walsh-Haar

Column Haar-Walsh

Binary distributed run length noise

(1-10)

0 0 0 0 0 0


(5-50)

1.963 2.568 2.374 1.945 2.088 2.766


(50-100)

2.433 2.239 2.015 2.261 2.059 2.282

Gaussian distributed run

length noise

2.087 2.207 2.037 2.243 2.109 2.413

Noise Type Row

DCT-

Walsh

Row Walsh-

DCT

Row DCT-

Haar

Row Haar-

DCT

Row Walsh-

Haar

Row Haar-

Walsh


(1-10)

5.755 4.897 4.036 3.840 6.381 3.961


(5-50)

5.411 4.702 4.676 4.316 4..140 4.234


(50-100)

3.656 3.430 3.512 3.011 3.101 3.632

Gaussian distributed run

length noise

2.097 1.419 1.97 1.299 1.349 1.640

DCT-Walsh Walsh-DCT

MAE=0.746 MAE=1.727 MAE=0.746 MAE=1.708

DCT-Haar Haar-DCT

MAE=0.746 MAE=2.209 MAE=0.746 MAE=2.970



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Table 3 shows that all hybrid transforms explored in proposed approach sustain noise addition attack

very strongly. Column hybrid transforms show better robustness over row hybrid transforms against binary

distributed run length noise attack.

D. Resizing attack

In resizing attack, watermarked image is first increased in size two times and then reduced to its

original size. This is achieved by three different mechanisms: bicubic interpolation, transform based zooming

[31] and grid based interpolation [32]. In transform based zooming, different transforms like DCT, DST, DFT,

Real Fourier Transform and Hartley transform are used to zoom and reduce the watermarked image. Fig. 6

shows result images for bicubic interpolation based resizing for column hybrid transforms used for embedding

the watermark.

Watermarked

image after

compression

Extracted

watermark

Watermarked

image after

compression

Extracted

watermark

MAE=3.770 MAE=18.886 MAE=3.766 MAE=20.349

DCT-Walsh Walsh-DCT

MAE=3.769 MAE=18.159 MAE=3.763 MAE=21.340

DCT-Haar Haar-DCT

MAE=3.768 MAE=19.437 MAE=3.762 MAE=20.842


Fig. 6: Results of various hybrid transforms against resizing using bicubic interpolation

Table IV shows average MAE between embedded and extracted watermark when different hybrid

transforms (column and row versions) are used to embed watermark.

Table IV Average MAE between embedded and extracted watermark against resizing attack

using various hybrid transforms Resizing type Column DCT-

Walsh Column Walsh-

DCT Column

DCT-Haar Column Haar-

DCT Column

Walsh-Haar Column Haar-

Walsh

Bicubic Interpolation

19.371 18.479 19.200 17.661 19.015 17.731

DFT 0.619 0.689 0.627 0.644 0.679 0.692

Grid based Interpolation

6.061 6.567 5.900 3.708 8.425 4.935

Resizing Type Row DCT-

Walsh

Row Walsh-

DCT

Row DCT-

Haar

Row Haar-

DCT

Row Walsh-

Haar

Row Haar-Walsh

Bicubic Interpolation

20.412 17.767 20.340 15.980 19.321 18.403

DFT 0.950 0.727 0.927 0.979 0.732 1.013

Grid based Interpolation

6.699 5.826 6.173 3.660 8.105 5.089


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From Table IV, it is observed that column as well as row hybrid transforms show excellent robustness

against resizing using DFT. For other transforms used to resize the watermarked image, MAE between

embedded and extracted watermark is found to be zero. Thus we can conclude that proposed watermarking

approach is strongly robust against transform based image resizing attack. Next high level robustness is obtained

against resizing using grid based interpolation as shown in Table 4. For resizing using bicubic interpolation the

quality of extracted watermark is acceptable. Similar results are obtained for row hybrid transforms also.

E. Histogram Equalization

Fig. 7 shows result images of Mandrill after equalizing its histogram for various column hybrid

transforms.

Watermarked

image after

compression

Extracted

watermark

Watermarked

image after

compression

Extracted

watermark

MAE=23.223 MAE=72.655 MAE=23.218 MAE=78.530

DCT-Walsh Walsh-DCT

MAE=23.223 MAE=72.651 MAE=23.208 MAE=79.643

DCT-Haar Haar-DCT

MAE=23.218 MAE=78.091 MAE=23.215 MAE=71.060


Fig. 7: Results of various hybrid transforms against histogram equalization

As can be seen from Fig. 7, MAE values between embedded and extracted watermark are higher due to

changes in their pixel intensity values. Similar behaviour is depicted by row versions of hybrid transforms.

VI. PERFORMANCE COMPARISON WITH HYBRID WAVELET TRANSFORMS Performance of proposed approach using hybrid transforms is compared with our previous work of

hybrid wavelet transforms.

A. Compression attack:

1) Column hybrid wavelet vs. Column hybrid transform

Fig. 8 shows comparison of column hybrid wavelet transforms and column hybrid transforms against

compression attack.


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(a)DCT-Walsh hybrid wavelet vs. DCT-Walsh

hybrid transform

(b)Walsh-DCT hybrid wavelet vs. Walsh-DCT

hybrid transform

(c)DCT-Haar hybrid wavelet vs. Haar-DCT hybrid

transform

(d)Haar-DCT hybrid wavelet vs. Haar-DCT hybrid

transform

(e)Walsh-Haar hybrid wavelet vs. Walsh-Haar

hybrid transform

(f)Haar-Walsh hybrid wavelet vs. Haar-Walsh

hybrid transform

Fig. 8: Column hybrid wavelet transforms vs. column hybrid transforms against compression attack.

From Fig. 8 it can be observed that hybrid transforms perform better than hybrid wavelet transforms.

For transform based compression this improvement is from 6% to 95%. For JPEG compression it is 23% to 38%

better. For VQ based compression the improvement in robustness by hybrid transforms is 20% to 44%.

2) Row hybrid wavelet transforms vs. row hybrid transforms Fig. 9 shows comparison of row hybrid wavelet transforms and row hybrid transforms against

compression attack. Similar to column hybrid transforms, row hybrid transforms improve the robustness against

compression attack by more or less similar range.


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hybrid transform


hybrid transform


transform


transform


hybrid transform


hybrid transform

Fig. 9: Row hybrid wavelet transforms vs. row hybrid transforms against compression attack. B. Cropping attack

1) Column hybrid wavelet transforms vs. column hybrid transform

Fig. 10 shows comparison of column hybrid wavelet transform and column hybrid transforms against

cropping attack. From Fig. 10 it is observed that hybrid transforms cannot perform better than hybrid wavelet

transforms in column version against compression attack. Hybrid wavelet transforms are much better in

robustness.


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hybrid transform


hybrid transform


transform


transform


hybrid transform


hybrid transform

Fig. 10: Column hybrid wavelet transforms vs. column hybrid transforms against cropping attack.

2) Row hybrid wavelet transforms vs. row hybrid transforms

Fig. 11 shows comparison of row hybrid wavelet transforms and row hybrid transforms against

cropping attack. Observations for row hybrid wavelet transforms and hybrid transforms are similar to that of

column transforms. Hybrid wavelet transforms better sustain against cropping attack than hybrid transforms.

(a)DCT-Walsh hybrid wavelet vs. DCT-Walsh (b)Walsh-DCT hybrid wavelet vs. Walsh-DCT


87

hybrid transform hybrid transform


transform


transform


hybrid transform


hybrid transform

Fig. 11: Row hybrid wavelet transforms vs. row hybrid transforms against cropping attack.

C. Noise addition attack

1) Column hybrid wavelet transform vs. column hybrid transform Fig. 12 compares column hybrid transforms with column hybrid wavelet transforms against noise

addition attack. In column version of hybrid transforms and hybrid wavelet transforms, MAE obtained for

smaller run length (1 to 10) of binary distributed run length noise is zero. Therefore it is not shown in the graph.

However, for row transforms, it is nonzero and hence can be compared.

From Fig. 12 it is observed that all hybrid transforms show up to 70% improved robustness against

binary distributed run length noise with run length 5 to 50 and 10 to 100. But for Gaussian distributed run length

noise, hybrid wavelet transforms are more robust.


hybrid transform


hybrid transform


88


transform


transform


hybrid transform


hybrid transform

Fig. 12: Column hybrid wavelet transforms vs. column hybrid transforms against noise addition attack.

2) Row hybrid wavelet vs. row hybrid transforms

Fig. 13 compares row hybrid transforms with row hybrid wavelet transforms. Behaviour of row hybrid

transforms and row hybrid wavelet transforms is opposite to that of column transforms. Thus in row version,

hybrid transforms perform better than hybrid wavelet transform against Gaussian distributed run length noise.

For Binary distributed run length noise, hybrid wavelet transform show better robustness than hybrid transforms.


hybrid transform


hybrid transform

(c)DCT-Haar hybrid wavelet vs. Haar-DCT hybrid (d)Haar-DCT hybrid wavelet vs. Haar-DCT hybrid


89

transform transform


hybrid transform


hybrid transform

Fig. 13: Row hybrid wavelet transforms vs. row hybrid transforms against noise addition attack.

D. Resizing attack

1) Column hybrid wavelet transforms vs. column hybrid transforms

Fig. 14 compares column versions of hybrid wavelet and hybrid transforms against resizing attack.

Hybrid transforms improve the robustness significantly up to 32% against bicubic interpolation based resizing

and up to 56% against resizing using DFT. For the combination of Walsh-DCT, Haar-DCT and Walsh-Haar,

hybrid wavelet transforms are more robust than hybrid transforms against resizing using grid interpolation.


hybrid transform


hybrid transform


transform


transform


90


hybrid transform


hybrid transform

Fig. 14: Column hybrid wavelet transforms vs. column hybrid transforms against resizing attack.

2) Row hybrid wavelet transforms vs. row hybrid transforms

Fig. 15 compares hybrid wavelet transforms and hybrid transforms against resizing attack in their row

versions. Performance of row versions is similar to that of column versions. Hybrid transforms are more robust

than hybrid wavelet transforms.


hybrid transform


hybrid transform


transform


transform


hybrid transform


hybrid transform


91

Fig. 15: Row hybrid wavelet transforms vs. row hybrid transforms against resizing attack.

VII. CONCLUSIONS In the proposed approach of watermarking using hybrid transforms, desirable characteristics of two

transforms are clubbed in one transform by taking their kronecker product. Hybrid transforms in their column

and row versions improve the performance of individual component transforms. At the same time they also

show significant improvement in robustness against various attacks over hybrid wavelet transforms. For

different attacks percentage improvement shown by hybrid transforms is given in following Table V.

Table V Performance improvement by hybrid transforms over hybrid

Wavelet transforms against various attacks.

Attack Percentage improvement over

hybrid wavelet transforms

Compression 59%

Cropping No improvement

Noise addition 70%

Resizing 32-56%

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